Janet has a jar of 54 coins consisting of dimes and quarters. If she has a total of $8.70, how many dimes does she have?

22

24

30

32

Question

Janet has a jar of 54 coins consisting of dimes and quarters. If she has a total of $8.70, how many dimes does she have?

 22

 24

 30

 32

mathstudent55 · Answer

Let the number of dimes = d
Let the number of quarters = q
Using d and q, what is the total number of coins?

whpalmer4 · Answer

You have two equations here.  Let D be the number of dimes, and Q be the number of quarters.  Then we know that $D + Q = 54$ because we have 54 coins, and they are only dimes and quarters.

Similarly, we know that a dime is worth 10 cents and a quarter is worth 25 cents.  Remembering that 1 dollar is 100 cents, can you write an equation in terms of D and Q that gives you the value of the coins, in cents?  With that equation and the first equation, you can solve for D and Q.

whpalmer4 · Answer

A slightly different way to write this would be strictly in terms of dimes.  There you would say you have D dimes.  Clearly, the number of quarters would be 54 - D.  Now you can write an equation using D for the number of dimes and 54 - D for the number of quarters, multiplying each by the value of the respective coin, and adding up to the total value.

whpalmer4 · Answer

Yet another way: figure out the value of 54 dimes and 54 quarters, respectively.  Compare the value of the jar ($8.70) with those two values.  If the value of the jar was 1/3 of the way between the extremes of 54 dimes / 0 quarters and 0 dimes / 54 quarters, the number of coins would also be 1/3 of the way.  Or you could "trade off" dimes for quarters until you got to the right value.  Start with 54 dimes = $5.40.  The number of coins remains constant, so every 4 quarters you add ($1) takes away 4 dimes ($0.40), meaning you can inch along the line by $0.60 for every 4 dimes converted to quarters.  $5.40, $6, $6.60, $7.20, etc.  When you get closer, you'll have to switch to trading off a single coin.

anonymous · Answer

22 dimes 26 quarters = 8.70

whpalmer4 · Answer

@Mpk15 Way to help the OP learn how to solve these problems!

anonymous · Answer

no problem

anonymous · Answer

its not 22 dimes.

mathstudent55 · Answer

22 dimes + 26 quarters = 48 coins
The problem states there are 54 coins.